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• I have confirmed this bug exists on the main branch of pandas.

Reproducible Example

df = pd.DataFrame({"a": range(1000)}) df.a = 1.2345678 * df.a df["b"] = df.a.astype("float16") df.describe() ab count1000.0000001000.0000 mean616.666616inf std356.567176inf min0.0000000.0000 25%308.333308308.4375 50%616.666616616.7500 75%924.999924924.8750 max1233.3332321233.0000

Issue Description

when change the column to low float format, the mean or std will calc wrong. In this case mean ,616 to inf. and in some case will result NaN. such as (but there is no NaN value in the column):
count 674522.000000
mean NaN
std 0.000000
min -17.359375
25% -1.610352
50% -0.280029
75% 1.049805
max 19.984375

Expected Behavior

same as normal mean or std

Installed Versions

/home/terry/.local/lib/python3.8/site-packages/_distutils_hack/init.py:30: UserWarning: Setuptools is replacing distutils.
warnings.warn("Setuptools is replacing distutils.")
Output exceeds the size limit. Open the full output data in a text editor

INSTALLED VERSIONS

commit : 87cfe4e
python : 3.8.10.final.0
python-bits : 64
OS : Linux
OS-release : 5.15.0-46-generic
Version : #49~20.04.1-Ubuntu SMP Thu Aug 4 19:15:44 UTC 2022
machine : x86_64
processor : x86_64
byteorder : little
LC_ALL : None
LANG : en_US.UTF-8
LOCALE : en_US.UTF-8

pandas : 1.5.0
numpy : 1.22.4
pytz : 2022.1
dateutil : 2.8.2
setuptools : 62.1.0
pip : 22.2.2
Cython : 0.29.30
pytest : 7.1.2
hypothesis : None
...
xlrd : 2.0.1
xlwt : None
zstandard : None
tzdata : 2022.1